GROUND STATE SOLUTIONS OF POLYHARMONIC EQUATIONS WITH POTENTIALS OF POSITIVE LOW BOUND

The purpose of this paper is threefold. First, we establish the critical Adams inequality on the whole space with restrictions on the norm [Formula Presented] for any τ > 0. Second, we prove a sharp concentration-compactness principle for singular Adams inequalities and a new Sobolev compact embedding in W^m;2(ℝ^2m). Third, based on the above results, we give sufficient conditions for the existence of ground state solutions to the following polyharmonic equation with singular exponential nonlinearity [Formula Presented] where 0 < β < 2m, V(x) has a positive lower bound and f(x; t) behaves like exp(α|t|²) t → +∞. Furthermore, when β = 0, in light of the principle of the symmetric criticality and the radial lemma, we also derive the existence of nontrivial weak solutions by assuming f(x, t) and V(x) are radially symmetric with respect to x and f(x,t) = o(t) at origin. Thus our main theorems extend the recent results on bi-Laplacian in ℝ⁴ by Chen, Li, Lu and Zhang (2018) to (-Δ)^m in ℝ^m.